Algorithm 867: QUADLOG—a package of routines for generating Gauss-related quadrature for two classes of logarithmic weight functions

ABSTRACT

A collection of subroutines and examples of their uses are described for the quadrature method developed in the companion article. These allow the exact evaluation (up to computer truncation and rounding errors) of integrals of polynomials with two general types of logarithmic weights, and also with the corresponding nonlogarithmic weights. The recurrence coefficients for the related nonclassical orthogonal polynomials with logarithmic weight functions can also be obtained. Tests of accuracy on various platforms are presented.

The routines are usable from Fortran, C, and C++ programs conforming to any of at least six international programming-language standards.

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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.2 Approximation
          Subjects: Special function approximations

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.4 Quadrature and Numerical Differentiation
          Subjects: Gaussian quadrature
  G.4 MATHEMATICAL SOFTWARE
      Subjects: Certification and testing; Reliability and robustness; Algorithm design and analysis; User interfaces; Documentation

Keywords:
EISPACK pythag() function, Gauss-Chebyshev quadrature, Gauss-Jacobi quadrature, Gauss-Laguerre quadrature, Gauss-Legendre quadrature, Gauss-type quadrature, Maple symbolic algebra system, Mehler quadrature, gamma-function testing, logarithmic integrals, machine-epsilon testing, orthogonal polynomials, psi-function testing, software portability, software testing